A218580 Triangle read by rows: T(n,k) is the number of ascent sequences of length n with first occurrence of the maximal value at position k-1.

1, 1, 1, 1, 2, 2, 1, 4, 5, 5, 1, 8, 13, 15, 16, 1, 16, 35, 47, 56, 62, 1, 32, 97, 153, 204, 248, 279, 1, 64, 275, 515, 770, 1030, 1257, 1423, 1, 128, 793, 1785, 3000, 4424, 5869, 7140, 8100, 1, 256, 2315, 6347, 12026, 19582, 28293, 37058, 44843, 50887

Offset: 1

Author

Joerg Arndt, Nov 03 2012

Keywords

• nonn
• tabl

Comments

Row sums are A022493.

Second column are powers of 2.

Examples

			Triangle starts:
[ 1]  1,
[ 2]  1, 1,
[ 3]  1, 2, 2,
[ 4]  1, 4, 5, 5,
[ 5]  1, 8, 13, 15, 16,
[ 6]  1, 16, 35, 47, 56, 62,
[ 7]  1, 32, 97, 153, 204, 248, 279,
[ 8]  1, 64, 275, 515, 770, 1030, 1257, 1423,
[ 9]  1, 128, 793, 1785, 3000, 4424, 5869, 7140, 8100,
[10]  1, 256, 2315, 6347, 12026, 19582, 28293, 37058, 44843, 50887,
...
		

Crossrefs

Cf. A022493 (number of ascent sequences).

Cf. A218579 (ascent sequences with last zero at position k-1), A218581 (ascent sequences with last occurrence of the maximal value at position k-1).

Cf. A137251 (ascent sequences with k ascents), A218577 (ascent sequences with maximal element k), A175579 (ascent sequences with k zeros).